Essays on Algebra

Application of Algebra in computing

Algebraic principles are used extensively in computing. In computer science, the computer algebra is called algebraic computation or symbolic computation. This is used mainly in software development and the associated algorithms that are used in the manipulation of mathematical expressions and objects. Kaltofen Erich (1982) noted that the long-known algorithms that were being used proved to be very long and this necessitated the revisiting of classical algebra with the intention of making them effective and efficient. In specific terms, algebra is used in the following fields of computing.
Encoding: in encoding, data that is arranged in arrays or matrices Continue reading...

Principal concept analysis may be defined as the statistical analysis tool relevant for the transformation of detailed or complex data into simple and easy to understand data. The method focuses on the use of principal components of statistics for possible interpretations. In most cases, the method does not include statistical assumptions. However, the method will always give extremely significant results for data that contains multivariate normal distribution. The data is extensively significant in determining the hypothetical variables or components that are extensively useful in the multidimensional data. In other words, the method PCA is a method significant in projecting Continue reading...

The fundamental theorem of algebra (FToA) is states that each non-constant single-variable polynomial with complex coefficients has at least one complex root. In fact, there are many equivalent formulations, such as this: every real polynomial can be represented as a product of real linear and real quadratic factors.
Early studies equations by al-Khwarizmi (from 800) are devoted only to positive real roots and have no relation to the FToA. Cardano was the first to realize that it is possible to work with the values ​​more general than real numbers (Geuvers, Wiedijk & Zwanenburg, 2002). This discovery was made in the Continue reading...

Solving Real-World Problems Using Algebra.

A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P= -25x2+300x . What number of clerks will maximize the profit, and what is the maximum possible profit?

Solution

The Quadratic equation P= -25x2+300x can be modified to the form y= -25x2+300x, where P= y.
Modifying the equation in this form enables us to plot the function y= -25x2+300x

For various values of x where x is a positive integer.

The general equation of a quadratic is given by y= ax2+bx+c where a, b and c Continue reading...

Kirchhoff’s Laws are fundamental in the analysis of electrical and electronic circuits. They describe the behavior of linear circuits accurately, and work well with approximations in other types of systems as well, making them extremely useful (“Electrical Principles”, 2013). Further, they are more popular and widely used than Maxwell’s equations, from which they can be derived. This is because Maxwell’s equations are very complex and involve brute Mathematics to solve even simple circuits, while the Kirchhoff’s laws are relatively much easier to use in most cases.

There are two laws which were given by Kirchhoff:

1) Kirchhoff’s Current law (KCL)
2) Kirchhoff’s Continue reading...

Given Traffic Scenario

Figure 1: The intersections of five one-way streets
1) There are five streets making six intersections. All the streets are one-way, that is, cars can move along only one direction on any street. The number of cars between intersections is the taken to be the traffic flows. For optimal flows, it is assumed that the number of cars entering an intersection in a given time must equal the number of cars leaving that intersection in that time. Also the number of cars entering and leaving any street per unit time is as mentioned in Figure 1. It is important Continue reading...

Mathematics and sciences gave me one of the biggest challenges in my early education life. Having studied in a private school in the US where I was introduced to Everyday Math, I realized that it was not as easy as the tutors would want us to believe. An s early as I can remember, the educators used old and ineffective teaching criteria. Having to count from 0 to 1000 and playing games seemed tedious at the moment but it was as much impractical as I would learn later on. Addition and subtraction facts were scanty, and less emphasized. Until Continue reading...

A.1A single mom has to go back to work and needs day care for her baby. She is trying to decide between a baby sitter, who cares for children in her home,ora nearby day care center. The baby sitter charges a flat rate of $10 per hour, and the localday carecenter charges $325 per week, for 5 days per week, up to 40 hours. (Mon-Fri), plus $10 per hour for any time exceeding 40 hours.
A.2The baby’s mom will need day care services M-F from 7:30-5:30 (10 hours per day, or 50 hours per week).
A.3The baby Continue reading...

<Student’s name><Professor’s name><Course number>
<The date of the paper>

Part 1. Data collection.

Gather from credible sources the following data:

- The amount of calcium and iron (in milligrams) found in one 10 oz package of broccoli
- The amount of calcium and iron (in milligrams) found in a ½ cup of frozen corn
- The recommended daily values (in milligrams) of calcium and iron
We have found that in 10 oz broccoli there are 116.44 mg of calcium and 2.04 mg of iron.
Also we found, that in 1 cup of frozen corn there are 3.28 mg of Continue reading...

Karl Theodor Wilhelm Weierstrass was a German mathematician who is often called as the "father of modern analysis".

Weierstrass was interested in the soundness of calculus, and also made significant advancements in the field of calculus of variations. Among the several significant axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems.
As we know, Cauchy gave a form of the (ε, δ)-definition of limit, in the context of formally defining the derivative, in the 1820s, but did not correctly distinguish between continuity at a point versus uniform continuity on an interval, due to insufficient rigor. Notably, in his 1821 Cours d'analyse, Cauchy gave a famously incorrect proof that the (pointwise) limit of ( Continue reading...

This is a report paper which provides a brief summary of introduction to linear algebra by John R. Durbin. The paper shall provide a brief summary of the three chapters of the book; chapter 11, 12 and thirteen.

Introduction

Modern algebra has been causing much difficulty to the learners and the professors as well. This is attributed to the complexity of the unit and elaborative theorems and formula used in the unit .therefore in this papers I have tried to simplify the theorems and formulas to easen the understanding of the topics such as Galois theorems permutation and many more. Continue reading...

Corse title:

1.
Using Boolean algebra laws, a negation is denoted by a NOT gate in the circuit. Assume the input signal at X is 1. As it passes the NOT gate it becomes 0. Using Boolean algebra, note that NOT gate is a negation of the input signal, which is 1, hence the output becomes 0. This 0 is the input of the OR gate. This similar to the Y but, at Z the signal is not affected since there is no negation by NOT gate. The truth table for OR is a mathematical representation of Boolean algebra on logics Continue reading...

Introduction

Islam also has a glorious and great history and heritage that has shaped the modern civilization in the West, including culture, education, and scientific developments. Unlike other religions such as Christianity where science and religion form two separate entities, the study of science has always been compatible with Islam religion. One such contribution is found in the field of mathematics where Muhammad bin Moosaa Al-Khawaarizmi is credited as one of remarkable founders of Algebra. He introduced the basic algebraic methods of balancing and reduction, and developed a number of formulas for solving such problems. In such a way, he Continue reading...

Thesis Statement

Algebra is one of the broadest terms used in the field of mathematics with its application in real life situations traceable way back in the ancient Babylonian times over four thousand years ago. The development of algebra was based on finding a solution to solving arithmetic equations mostly in the religious rituals and dilemmas. Most of the renown historical mathematicians such Rene Descartes made some of the major contributions to the development of the modern algebra whereby he came up with la geometre, a publication which focused on improving problem solving techniques in the field of geometry. However, the Continue reading...

According to Stanoyevitch (2010), cryptography refers to one of the oldest branches of pure mathematics that primarily deal with the study of integers. It deals with the prime numbers and also the properties of the objects which are made out of the integers like the algebraic integers. Cryptography is a very important tool for protecting information from unauthorized access in the computer systems. Currently, finite fields are becoming very vital in cryptography. Most cryptographic algorithms depend heavily on the properties of the finite fields especially the elliptic curve cryptography and the Advanced Encryption Standard (AES). The most important concepts Continue reading...

Muhammad ben Musa al-Khwarizmi

Muhammad ben Musa al-Khwarizmi was a Persian astrophysicist, geometrician, and geographer. He was born in Persia at around 780 and died around 850. Though his name signifies that his family was originally from the region around Khwarizmi nearby the Aral Sea, historians trust that al-Khwarizmi was congenital in the town of Baghdad, which the current day Iraq. Though diminutive is identified about his cloistered life, al-Khwarizmi’s effort and participation have principally endured the ages discreetly intact. The exclusion is a volume of mathematics in which the novel cannot be established; there is, though, a Latin rendition of his Continue reading...

Introduction:

A linear equation is an algebraic equation in which the highest power of the unknown variable is a unit. Linear equation is in the form of where a, b and c are constants and x and y are the variables of the equation (PBS. Mathline). A linear equation produces a straight line graph when plotted to scale on a graph paper.

Solving a System of Linear Equations

A system of equations is the case when we have more than one linear equation. (When there are two or more equations). For elementary studies, the number of unknowns in the system is equal to the number of Continue reading...

Question 1

R { 1,2,3,4 }
Z { 5,6,7,8 }
F is a subset of RZ
Where each element X ∈ R
and each element Y ∈ Z
(x, y) ∈ F

F subset { y ∈ Z| ( x, y) ∈ F for some x ∈ R}

R is the domain

Z is the codomain

, (4), ∈ Z

2.65 to 6.65

On the graph point 2.65 is (2.65, 4)

And point 6.65 is (6.65, 4)
x ∈ Z y ∈ R
( x, y ) ∈ F is a subset of RZ
Using = 4 Transforming R along itself

R ( 2.65, 4 )

F( 6.65, 4 )
R + Z defines a function since each element of R occurs only once among the ordered pairs.
Where set:
R is the domain of the function

Z is the codomain Continue reading...

The paper analyzes and discusses different concepts related to Algebra. The paper talks

about Order of Operations, Linear equations and their application, linear inequalities,

Quadratic equations. It talks about and summarizes different methods of tackling and

simplifying such algebraic expressions. Finally the paper dwells into different functions and

their graphic representations.

Algebra and Functions

Order of Operations: Order of operations is a mathematical that determines the

correct order for solving any of math operations. Powers and roots are solved before

multiplication and division, which in turn are solved before addition and subtraction

(Toolingu, n.d.). The rule is used in calculation and simplification of a complex algebraic

expression involving many arithmetic operations. Order Continue reading...

This discussion post or essay has basically been undertaken to understand some standard

results in Algebra in Mathematics. We would analyze the importance of using derived and

standard results and also about how they ease our calculations drastically. We would also

learn about some elementary but very important terms like Exponents, Integers etc. and

their usage with respect to solving questions in Algebra.

Here in the given questions we have got three variables namely a, b, c which have been

assigned values according to the problem statement (based on my date of birth). All three

variables are integers with ‘b’ being the lowest term and hold the following values:

a= 8
b=-2
Continue reading...

Quantitative Research methods in statistics

The paper focuses on analyzing the use of research methods in Okello’s article “learning and Teaching college algebra at University level: Challenges and opportunities- A case study of USIU”, published in Journal of Language, Technology &entrepreneurship in Africa. Application of quantitative and qualitative methods in research (experimental and non experimental) studies is crucial for obtaining valid and reliable information. Quantitative methods or techniques lie within the interval estimation and hypothesis testing categories (Nadezhda , 2010). In interval estimation, statistics are used to estimate the interval for which the true parameter of a population lies from a representative sample. On Continue reading...

In algebra the definition given to a monomial and a polynomial is that a monomial is a product of positive integer powers of similar or different variables. It has only one term and does not contain a variable in its denominator. A polynomial is the sum of one or more like or unlike terms. Polynomials are generally written in descending order and they are in their simplest form when they contain no like terms.
Distributive property also known as distributive law is basically breaking down numbers; separating like and unlike terms thus putting like terms together as well as Continue reading...

1) Example (Every day business) Saving for the Future

You will graduate from high school in four years and go on to college. To help you pay for college books your grandparents put $1500 in a bank account paying 4.5% simple interest. When you go to college the money will have been in the account for 12 years. How much money will you have?

Step 1. PVrt = INT where INT = Interest and PV = Present Value
Step 2. FV = PV + INT = PV(1 + rt) where FV = Future value, r = annual interest rate, and
t = years Continue reading...

Question 1

A. What is similarities and differences do you see between functions and linear equations studied in Ch. 3?

Functions and linear equations have elements which create straight lines when plotted on the graph. Both linear equation and a function are polynomial to the first degree. A linear equation and function have variables that are paired and separated by comma in a bracket. The variables are normally in form of x and y with each having one value. A linear equation is an algebraic expression having two variables with similar value while a function has only one variable. Continue reading...

Discussion Question

According to the classical definition, order of operations is a sequence of actions needed for the salvation of a mathematical problem. It defines which procedures should be performed first in order to receive a correct final result.

Simple order rules assume the next terms:

1) Calculation should be completed starting from the left,
2) Results in brackets should be done first, then go the exponents,
3) Multiplication and division should be done in the order as operations occur,
4) Addition and subtraction should also be done in the way the operations occur.

Example: 4* (10-5) +3.

1) Continue reading...

Part A Difference between equation and expression

Expression

Equation

1. Do not contain equal signs
2. Formed by variables, mathematical operation signs, constants,
3. An expression can only be simplified
4. Variables in expressions do not represent specific constant values Continue reading...

- Problem Statement – Area(s) of Improvement
In any educational process the only way for a student to learn is by actually remembering what they have been taught. This is doubly true in any of the more precise subject such as math, science and technology; all of which rely on solid evidence to prove someone’s point and more importantly, numbers. By this very attribute, math has gained the ire of students around the world despite the numerous improvements and possibilities the field has provided to society.
In this light, the main problem that this research paper is trying to Continue reading...

Query optimizer architecture

Given a database and a query on it, there a number of processes through which the query is run through with all the processes having different execution plans. In the optimization process the best plan is selected after careful consideration of all the option plans available.
Query optimizer architectural definition gives a better understanding of the tests that are done on the alternatives give (Epstein, 2008). Below is a simple architectural view of the query optimization process.

In the simple architecture Continue reading...

Introduction

Undeniably, primordial Egyptians’ mathematics is one of the earliest kinds of mathematics which had a great influence of the entire traditions of mathematics that followed later. In this context, the term “Egyptian math” is used to refer to math that has been written using the Egyptian language. The work of Egyptians represents one of the civilizations that began taking advantage of the benefits of mathematics as well as numbers; which is evident based on the fact that the results of this early mathematics are still noticeable in the immense architectural accomplishments of Continue reading...

Introduction

The Hindu-Arabic numerals are said to have come from the Hindus, Egyptians, Persians and Arabs. There is a presumption that the interrelation between traders served in carrying the symbols from one region to another and hence the accumulation from the different origins. Nonetheless, India is said to be the country that first used the largest number of numerals. The numeral system was established in ancient India. Prior to the emergence of Arab Empire the numeral system of the Hindu and Arabs was already going towards the West. The Arabs adopted the nine numerals in the 9th century. Initially, it Continue reading...

Impact of Technology on Supporting First Grade Students’ Creative Thinking in Mathematics

Abstract:
This research provides an in-depth examination of the impact of technology in supporting the acquisition of mathematical creative thinking skills among first-grade student. It examines how technology can be properly integrated with mathematics to promote math’s performance without declining creative thinking skills in mathematics among the elementary students.
Social constructivism theory as the method of learning in first-grade mathematics students is advocated; it defines the developmental stages of a child and relates to his or her learning and problem-solving ability. Its requirements can properly be integrated to Computer-aided learning processes.
The value and importance of common core Continue reading...

CRITIQUE OF “THE ALGEBRA OF INFINITE JUSTICE”

The Algebra of infinite justice is an article written by Arundhati Roy. Arundhati was born on Novemeber 24, 1961 in Shillong to a Bengali Hindu father and a Christian mother. She won a Booker Prize for her first novel-The God of Small Things in 1997. After that she wrote on many topics on politics, nuclear weapons s in India, corruption among others. One of her writing is “The algebra of infinite justice” where she criticizes the role of USA in the beginning, propagation, and methods to fight terrorist. She claims the USA is created terrorist and is attempting to Continue reading...

The article, “Predicting Human Brain Activity Associated with the Meanings of Nouns” was written by Tom M. Mitchel, Svetlana V. Shinkareva and their five associates. The article was published in Science in May 2008. It outlined a computational program that predicted which parts of the brain were stimulated and would respond to certain words and images, or certain stimuli. I found several concepts of the article very interesting. For example, the basis of the article’s studies was founded on creating a computational framework subject to linguistics. In layman terms, a grid of the mind was drawn up, based Continue reading...

QUESTION 1

Function – A function is the relationship that exists between an input and output such that one input has only one possible output. This implies that a function takes an input and produces an output based on the input (Cheney & Kincaid, 2012).

Examples

Linear function
y = 2 x

Quadratic function

y = 2 x2

Third degree polynomial

y = 2 x3

Exponential function

y = e2x

Logarithmic function

y = log 2 x

Periodic function

y = sin x
Domain of a function - The domain of a function is the set of inputs for which the output of the function exists (Cheney & Kincaid, 2012).The domain of linear function is (- ∞ to ∞), quadratic function is (- ∞ Continue reading...

“An educated Petersburg, is a successful Petersburg”

Introduction
Petersburg is an independent American city found in the Virginia state of the United States. Its population is overwhelmingly black with an estimated percentage of 79. The city has got a rich industrial history and once supported a booming tobacco industry. Petersburg boasts of several schools in all learning levels.

Overview of the campaign

Generally, Petersburg education standards are adversely reviewed in all quarters. This is a view well rooted in the collective mind of the nation. Recently, a study was conducted on the relationship of education standards and affluence. It was noted that poorer kids do worse than their richer counterparts. Continue reading...

Introduction

Pythagoras theorem is named after a Greek mathematician Pythagoras who lived in 475BC. Despite the theorem being named after him, he was not the only ancient person who came up or probably used the theorem because the Babylonians and used it in ancient civilization. In the theorem Pythagoras creates a relationship between the hypotenuse and two sides of a right angled triangle as a2 + b2 = c2. Later on, mathematician from north Europe came up with Pythagoras triples to simplify on ways of obtaining sides of right angled triangles. As years went by, different mathematicians came up with different was Continue reading...

Modern American fiction often concerns itself with identity; the individual is often at stake in part of a larger group, whether it be a family, village, or the societies of a big city. Perhaps it is the very nature of American fiction to place identity at the core of much of its short fiction; as a relatively young country that evolved quickly through colonial times and the industrial revolution, its population comes from around the world yet still seeks to define itself as a nation. Therefore, it is no surprise that in the diverse fiction of America, the theme Continue reading...

Inventory management

As Wooden Wonders Ltd, adopting a good model of inventory management would optimize inventory order quantity and re-order level for the company. It is known that inventory plays a very important role in the supply chain. With a good model, the need for inventory would be minimized since the model is supposed to manage the factors that make inventory levels to go up. The items that require inventory are split in two main categories. The first is dependent demand items while the second is independent demand items. The systems required to manage these two categories vary.

Wooden Wonders, which Continue reading...

Abstract

Research into how individuals learn and the different stages of learning has been the focus of studies by various scholars. Based on the research that has been conducted so far, there are several theories that have been advanced. Notable among these theories are the theories that have been advanced by Piaget and Lev Vygotsky. They both concur on the role of the surrounding environment on the learner but differ on the effect. In spite of the differences that are evident in their theories they have been instrumental in shaping the teaching styles that are applies all over the world. Continue reading...

Abstract

The element of teacher bias in the education institutions is of great significance to the educational development of the students. It is important in the sense that it provides insights into the role of the integration of the students and the teachers for educational success. Research has been conducted to determine the potential effects of the teacher bias on the educational achievement of the students. This research encompassed both the qualitative and the quantitative methods in identifying these concepts. Classroom observations were conducted for the research and results drawn and analyzed from the data. The results of this research Continue reading...